Discrete & Computational Geometry

, Volume 22, Issue 1, pp 149–158

Spatial Graphs and Oriented Matroids: the Trefoil

  • J. L. Ramirez Alfonsin


Let m=m(K) be the smallest positive integer such that every linearspatialrepresentation of the complete graph with n vertices, n ≥ m , contains either the knot K or its mirror . In this paper we show that m(Trefoil)=7 . The proof uses the theory of oriented matroids.


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Copyright information

© 1998 Springer-Verlag New York Inc.

Authors and Affiliations

  • J. L. Ramirez Alfonsin
    • 1
  1. 1.Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior C.U., Mexico D.F. 04510MX

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